Gelfand–Naimark Theorem

(Theory)

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What is Gelfand–Naimark theorem?

In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an operator algebra.

Technology Types

mathematical theoremoperator theorypropositionstatementtheoremtheorems in functional analysistheory

Synonyms

Gel'fand-Naimark theoremGelfand Naimark theoremGelfand theoremGelfand-Naimark representation theoremGelfand-Naimark theorem

Translations

Satz von Gelfand-Neumark (de)Теорема Гельфанда — Наймарка (ru)ゲルファント=ナイマルクの定理 (ja)

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